Energy input spectra applicable to the seismic design of structures in moderate-to-high seismicity regions such as Colombia are proposed. They are derived from the bilinear envelope of individual spectra obtained for 144 ground motions recorded in Colombia. The spectra account for the increase of input energy due to the plastification of the structure in the short period region, through a new formula derived from extensive nonlinear analyses. The proposed energy input design spectra are compared with the provisions of the Colombian seismic code, and with those proposed for Japan, Iran and Greece. It is found that the proposed spectra are more demanding than the current Colombian seismic code, and that they are agree with those developed recently for six cities in Greece by applying a different approach. An empirical equation to estimate the portion of the seismic input energy that contributes to structural damage is also proposed.

This report presents the work done within the framework of my master thesis in the program Infrastructure Engineering at KTH Royal Institute of Technology, Stockholm. This project has been proposed and sponsored by the French company Setec TPI, part of the Setec group, located in Paris. The overall goal of this study is to investigate fluid-structure interaction and particularly sloshing in liquid-containing structures subjected to seismic or other dynamic action. After a brief introduction, the report is composed of three main chapters. The first one presents and explains fluid-structure interaction equations. Fluid-structure interaction problems obey a general flow equation and several boundary conditions, given some basic assumptions. The purpose of the two following chapters is to solve the corresponding system of equations. The first approach proposes an analytical solution: the problem is solved for 2D rectangular tanks. Different models are considered and compared in order to analyze and describe sloshing phenomenon. Liquid can be decomposed in two parts: the lower part that moves in unison with the structure is modeled as an impulsive added mass; the upper part that sloshes is modeled as a convective added mass. Each of these two added mass creates hydrodynamic pressures and simple formulas are given in order to compute them. The second approach proposes a numerical solution: the goal is to be able to solve the problem for any kind of geometry. The differential problem is resolved using a singularity method and Gauss functions. It is stated as a boundary integral equation and solved by means of the Boundary Element Method. The linear system obtained is then implemented on Matlab. Scripts and results are presented. Matlab programs are run to solve fluid-structure interaction problems in the case of rectangular tanks: the results concur with the analytical solution which justifies the numerical solution. This report gives a good introduction to sloshing phenomenon and gathers several analytical solutions found in the literature. Besides, it provides a Matlab program able to model effects of sloshing in any liquid-containing structures.

En la presente tesis se ha desarrollado la evaluación estructural de cinco reservorios circulares del tipo apoyado, construidos entre los años 1977 y 1997, ubicados en zonas de alto riesgo sísmico en Lima Metropolitana y ubicados en suelos medianamente rígidos, con el objetivo de evidenciar si estas estructuras continúan conservando un diseño sísmico adecuado en base a los requerimientos sísmicos actuales, y por ende si serán capaces de resistir un evento sísmico severo y continuar con el servicio. Para poder modelar y determinar la respuesta de los se reservorios se empleó el modelo equivalente de Housner, obteniendo así la masa impulsiva y convectiva, modelado en el programa SAP2000 con ayuda de las normas ACI 350.3-06 y E.030. En cuanto a la determinación de las fuerzas resistentes, para poder realizar la evaluación estructural correspondiente, se utilizó la norma peruana E.060-2009 Concreto Armado, con la cual se obtuvo dichas fuerzas y se realizaron las verificaciones estructurales. Con respecto a los resultados de las verificaciones realizadas, se observó que los reservorios en estudio no mantienen un diseño estructural adecuado en cuanto a las solicitaciones sísmicas actuales. Estas deficiencias se plasman en déficit de refuerzo horizontal por corte en muros, cuantía mínima vertical por corte en muros, refuerzo en la base del muro por momento tangencial, armadura requerida en la viga collarín, y refuerzo en el extremo de la cúpula por tracción radial; por lo que estas estructuras, ante la presencia de un evento sísmico severo, se encuentran expuestas a presentar fallas estructurales. / In the present thesis has been carried out the structural assessment of five round ground concrete tanks, built between 1977 and 1997, and located in high seismic risk areas in Lima Metropolitana in moderately rigid soils, with the objective of demonstrating if these structures still preserve an adequate structural design base on the current standards and consequently, if they will be able to withstand a severe seismic event and, hence, continue with their service. In order to model and determine the response of the tanks, the Housner’s rigid equivalent model was used, obtaining this way the impulsive and convective masses, which were modeled in the software SAP2000 with the ACI 350.3-06 standard and the E.030 Peruvian standard. Regarding on the determination of the resistant forces, in order to carry out the corresponding structural evaluation, the Peruvian standard “Concreto Armado E.060” was utilized. With regard to the results of the verifications carried out, it was observed that the reservoirs under study do not maintain an adequate structural design in terms of the current seismic solicitations. These deficiencies are reflected in horizontal reinforcement deficit by shear force on the walls, minimum amount of vertical rebar by shear on the walls, reinforcement in the base of the wall by tangential bending moment, rebar required in the beam by radial tensile force, and rebar in the end of the dome by radial traction; so these structures, in the presence of a severe seismic event, are exposed to structural failures. / Tesis